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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

Local Poincaré algebra from quantum chaos

The local two-dimensional Poincaré algebra near the horizon of an eternal AdS black hole, or in proximity to any bifurcate Killing horizon, is generated by the Killing flow and outward null translations on the horizon. In holography, this local Poincaré algebra is reflected as a pair of unitary flows in the boundary Hilbert space whose generators under modular flow grow and decay exponentially with a maximal Lyapunov exponent. This is a universal feature of many geometric vacua of quantum gravity. To explain this universality, we show that a two-dimensional Poincaré algebra emerges in any quantum system that has von Neumann subalgebras associated with half-infinite modular time intervals (modular future and past subalgebras) in a limit analogous to the near-horizon limit. In ergodic theory, quantum dynamical systems with future or past algebras are called quantum K-systems. The surprising statement is that modular K-systems are always maximally chaotic. Interacting quantum systems in the thermodynamic limit and large N theories above the Hawking-Page phase transition are examples of physical theories with future/past subalgebras. We prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics and the exponential decay of (modular) correlators. We generalize our results from the modular flow to any dynamical flow with a positive generator and interpret the positivity condition as quantum detailed balance.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1996

Application of Hybrid Optimization-Expert System for Optimal Power Management on Board Space Power Station

The space power system has two sources of energy: photo-voltaic blankets and batteries. The optimal power management problem on-board has two broad operations: off-line power scheduling to determine the load allocation schedule of the next several hours based on the forecast of load and solar power availability. The nature of this study puts less emphasis on speed requirement for computation and more importance on the optimality of the solution. The second category problem, on-line power rescheduling, is needed in the event of occurrence of a contingency to optimally reschedule the loads to minimize the 'unused' or 'wasted' energy while keeping the priority on certain type of load and minimum disturbance of the original optimal schedule determined in the first-stage off-line study. The computational performance of the on-line 'rescheduler' is an important criterion and plays a critical role in the selection of the appropriate tool. The Howard University Center for Energy Systems and Control has developed a hybrid optimization-expert systems based power management program. The pre-scheduler has been developed using a non-linear multi-objective optimization technique called the Outer Approximation method and implemented using the General Algebraic Modeling System (GAMS). The optimization model has the capability of dealing with multiple conflicting objectives viz. maximizing energy utilization, minimizing the variation of load over a day, etc. and incorporates several complex interaction between the loads in a space system. The rescheduling is performed using an expert system developed in PROLOG which utilizes a rule-base for reallocation of the loads in an emergency condition viz. shortage of power due to solar array failure, increase of base load, addition of new activity, repetition of old activity etc. Both the modules handle decision making on battery charging and discharging and allocation of loads over a time-horizon of a day divided into intervals of 10 minutes. The models have been extensively tested using a case study for the Space Station Freedom and the results for the case study will be presented. Several future enhancements of the pre-scheduler and the 'rescheduler' have been outlined which include graphic analyzer for the on-line module, incorporating probabilistic considerations, including spatial location of the loads and the connectivity using a direct current (DC) load flow model.

Momoh, James↗

NASA NTRS1973

A more general system for Poisson series manipulation.

The design of a working Poisson series processor system is described that is more general than those currently in use. This system is the result of a series of compromises among efficiency, generality, ease of programing, and ease of use. The most general form of coefficients that can be multiplied efficiently is pointed out, and the place of general-purpose algebraic systems in celestial mechanics is discussed.

Cherniack, J. R.↗

NASA NTRS1999

Integrated Modeling Tools for Thermal Analysis and Applications

Integrated modeling of spacecraft systems is a rapidly evolving area in which multidisciplinary models are developed to design and analyze spacecraft configurations. These models are especially important in the early design stages where rapid trades between subsystems can substantially impact design decisions. Integrated modeling is one of the cornerstones of two of NASA's planned missions in the Origins Program -- the Next Generation Space Telescope (NGST) and the Space Interferometry Mission (SIM). Common modeling tools for control design and opto-mechanical analysis have recently emerged and are becoming increasingly widely used. A discipline that has been somewhat less integrated, but is nevertheless of critical concern for high precision optical instruments, is thermal analysis and design. A major factor contributing to this mild estrangement is that the modeling philosophies and objectives for structural and thermal systems typically do not coincide. Consequently the tools that are used in these discplines suffer a degree of incompatibility, each having developed along their own evolutionary path. Although standard thermal tools have worked relatively well in the past. integration with other disciplines requires revisiting modeling assumptions and solution methods. Over the past several years we have been developing a MATLAB based integrated modeling tool called IMOS (Integrated Modeling of Optical Systems) which integrates many aspects of structural, optical, control and dynamical analysis disciplines. Recent efforts have included developing a thermal modeling and analysis capability, which is the subject of this article. Currently, the IMOS thermal suite contains steady state and transient heat equation solvers, and the ability to set up the linear conduction network from an IMOS finite element model. The IMOS code generates linear conduction elements associated with plates and beams/rods of the thermal network directly from the finite element structural model. Conductances for temperature varying materials are accommodated. This capability both streamlines the process of developing the thermal model from the finite element model, and also makes the structural and thermal models compatible in the sense that each structural node is associated with a thermal node. This is particularly useful when the purpose of the analysis is to predict structural deformations due to thermal loads. The steady state solver uses a restricted step size Newton method, and the transient solver is an adaptive step size implicit method applicable to general differential algebraic systems. Temperature dependent conductances and capacitances are accommodated by the solvers. In addition to discussing the modeling and solution methods. applications where the thermal modeling is "in the loop" with sensitivity analysis, optimization and optical performance drawn from our experiences with the Space Interferometry Mission (SIM), and the Next Generation Space Telescope (NGST) are presented.

Milman, Mark H.↗

DOE OSTI2021

Distributed Data-Driven Power Iteration for Strongly Connected Networks

Here, this paper presents data-driven power iteration to distributively estimate the dominant eigenvalues of an unknown linear time-invariant system. The proposed strategy only requires a single trajectory data or measurements. Furthermore, in order to perform the distributed estimation, the communication network topology can be chosen to be any strongly connected directed graphs. The proposed data-driven power iteration is demonstrated using several numerical examples and is then applied to estimate the generalized algebraic connectivity of cooperative systems and to control the epidemic spreading.

Gusrialdi, Azwirman↗

DOE OSTI2023

Information loss, mixing and emergent type III 1 factors

A manifestation of the black hole information loss problem is that the two-point function of probe operators in a large Anti-de Sitter black hole decays in time, whereas, on the boundary CFT, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity. We call operators that cluster in time “mixing” and explore the necessary and sufficient conditions for mixing. The information loss problem is a special case of the statement that in type I algebras, there exists no mixing operators. We prove that, in a thermofield double state (KMS state), if mixing operators form an algebra (close under multiplication), the resulting algebra must be a von Neumann type III 1 factor. In other words, the physically intuitive requirement that all nonconserved operators should exponentially mix is so strong that it fixes the observable algebra to be an exotic algebra called a type III1 factor. More generally, for an arbitrary out-of-equilibrium state of a general quantum system (von Neumann algebra), we show that if the set of operators that mix under modular flow forms an algebra, it is a type III1 von Neumann factor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1989

Spatial operator algebra framework for multibody system dynamics

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

Rodriguez, G.↗

NASA NTRS1992

Spatial Operator Algebra for multibody system dynamics

Rodriguez, G.↗

NASA NTRS1985

Performance of direct and iterative algorithms on an optical systolic processor

The frequency-multiplexed optical linear algebra processor (OLAP) is treated in detail with attention to its performance in the solution of systems of linear algebraic equations (LAEs). General guidelines suitable for most OLAPs, including digital-optical processors, are advanced concerning system and component error source models, guidelines for appropriate use of direct and iterative algorithms, the dominant error sources, and the effect of multiple simultaneous error sources. Specific results are advanced on the quantitative performance of both direct and iterative algorithms in the solution of systems of LAEs and in the solution of nonlinear matrix equations. Acoustic attenuation is found to dominate iterative algorithms and detector noise to dominate direct algorithms. The effect of multiple spatial errors is found to be additive. A theoretical expression for the amount of acoustic attenuation allowed is advanced and verified. Simulations and experimental data are included.

Ghosh, A. K.↗

DOE OSTI2024

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗

NASA NTRS1999

Metrics for Labeled Markov Systems

Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.

Desharnais, Josee↗

DOE OSTI2025

Strongly nonlinear wave propagation in elasto-plastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are often prohibitively expensive at scales of interest. Prior studies have therefore utilized low-order effective medium models, such as discrete mass-spring lattices, to capture essential properties in the long-wavelength limit. While models of this type have been successfully implemented for a wide variety of nonlinear elastic systems, they have predominantly considered dynamics depending only on the instantaneous kinematics of the lattice, neglecting history-dependent effects, such as wear and plasticity. Here, to address this limitation, the present study develops a lattice-based modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history- and rate-dependent nature of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several models inspired by classical lattice dynamics and continuum plasticity theory and explore means to obtain empirical plasticity models for general geometries, thereby gaining insight into the influence of microstructural plasticity on effective material performance, which can be used to improve the design of nonlinear mechanical metamaterials.

Dynamic simulation↗

NASA NTRS1982

A general algorithm for solving the algebraic Riccati equation

The generalized eigenvalue problem provides a suitable framework for reliable solutions of many system theoretic, control, and estimation problems. A general algorithm for solving the matrix algebraic Riccati equation (ARE) which utilizes a pencil structure is described here. This algorithm avoids unnecessary inversion of cost or transition matrices, making it a numerically sound way to solve for the gains and/or ARE with singular quadratic costs, for cases satisfying detectability and stabilizability conditions. Examples are solution with discrete dead-beat control, noiseless measurements in Kalman filters and time-delays in discrete-time systems, which cause difficulties in the Hamiltonian standard eigenvalue problem formulation. The ARE algorithm implementatiton and numerical examples are shown.

Walker, R. A.↗

NASA NTRS1989

Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

The accuracy requirements of optical processors in adaptive optics systems are determined by estimating the required accuracy in a general optical linear algebra processor (OLAP) that results in a smaller average residual aberration than that achieved with a conventional electronic digital processor with some specific computation speed. Special attention is given to an error analysis of a general OLAP with regard to the residual aberration that is created in an adaptive mirror system by the inaccuracies of the processor, and to the effect of computational speed of an electronic processor on the correction. Results are presented on the ability of an OLAP to compete with a digital processor in various situations.

Downie, John D.↗

NASA NTRS1982

Automatic algebraic coordinate generation

A computer software system has been developed to automatically generate two-dimensional coordinates from algebraic transformations. For topologically complex regions, a smooth assembly of the transformations can be used to automatically produce a composite mesh where a general gridded format is retained. The algebraic mesh generation system consists of a collection of operator subroutines which are applied to an established data structure and which automatically perform the necessary parts of mesh construction from a sequence of multisurface transformations. The system operators are discussed, taking into account the data base, the order of application, direct surface generators, geometric surface operators, surface generators from existing surfaces, transverse operators, mesh operators, assembly operators, and data visualization operators. Attention is given to applications related to airfoils.

Eiseman, P. R.↗

NASA NTRS1993

Symmetry algebra of a generalized anisotropic harmonic oscillator

It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

Castanos, O.↗

DOE OSTI2022

Krylov subspace recycling for evolving structures

Krylov subspace recycling is a powerful tool when solving a long series of large, sparse linear systems that change only slowly over time. In PDE constrained shape optimization, these series appear naturally, as typically hundreds or thousands of optimization steps are needed with only small changes in the geometry. In this setting, however, applying Krylov subspace recycling can be a difficult task. As the geometry evolves, in general, so does the finite element mesh defined on or representing this geometry, including the numbers of nodes and elements and element connectivity. This is especially the case if re-meshing techniques are used. As a result, the number of algebraic degrees of freedom in the system changes, and in general the linear system matrices resulting from the finite element discretization change size from one optimization step to the next. Changes in the mesh connectivity also lead to structural changes in the matrices. In the case of re-meshing, even if the geometry changes only a little, the corresponding mesh might differ substantially from the previous one. Obviously, this prevents any straightforward mapping of the approximate invariant subspace of the linear system matrix (the focus of recycling in this work) from one optimization step to the next; similar problems arise for other selected subspaces. In this paper, we present an algorithm to map an approximate invariant subspace of the linear system matrix for the previous optimization step to an approximate invariant subspace of the linear system matrix for the current optimization step, for general meshes. This is achieved by exploiting the map from coefficient vectors to finite element functions on the mesh, combined with interpolation or approximation of functions on the finite element mesh. We demonstrate the effectiveness of our approach numerically with several proof of concept studies for a specific meshing technique.

42 ENGINEERING↗

NASA NTRS1975

Temperature fields of an absorptive medium in a radiating system of arbitrary configuration (the spatial problem)

A generalized zonal method based on systems of linear algebraic equations is used to determine the temperature fields in an absorptive grey medium filling a closed radiation system that consists of three boundary zones, of which one is adiabatic and the other two are isothermal. The example calculation considers the case of a solenoidal radiation field of local radiative equilibrium.

Surinov, Y. A.↗